Impedance-correcting network



Nov. 6, 1928. 1,690,233

^ K. KPFMLLER IMPEDANCE CORRECTING NETWORK Filed Aug. 23. 1921 rve; 0.2

Patented Nov. 6, 1928.

UNITED s'ra'ras PATENT OFFICE.

KARL KIPFMLLER, OF BERLIN -FRIEDENAU, GERMANY, ASSIGNOR` T0 SIEMENS &

. HALSKE AKTIENGESELLSCHAFT, OF SIEMENSSTADT, NEAR BERLIN, GERMANY, A u

n CORYORATION OF GERM/ANY.

IMPEDANCE-CORRECTING NETWORK.

Application led August 23, y1921, Serial No. 494,519, and in Germany September 10, 1919. (GRANTED UNDER. THE PRovIsIoNs or Tim ACT or MARCH s, 1921, 41 STAT. L., 131s.)y

I have filed applications as follows: Germany September 10, 1919, Patent No. 330,964;

Sweden September 2, 1920; Switzerland September 6, 1920; Italy September 10, 1920; Norway September 10, 1920. ,A z

The problem of simulating artificially the electric qualities of actual transmission lines occurs frequentlyxin telephony and telegraphy. For inst-ance, several reciprocal` repeater connections in telephonie or telegraphic lines require the simulation of the.

impedance of the transmission line.

For the usual aerial lines the solution of this problem presents no difficulties. The

`characteristic.impedance W of such a line is given approximately by the formula .Y E R (1) W \/c L zat/Lc In this formula L, C and R denote the kilometric values Vof the inductance, cap a city and ohmic resistance ofthe line; t: 1 and w thefre uency in cycles viz,the number of periods o the sinusoidal current within 211 sec. In the drawing, Fig. 1 shows a network for Y 'matching the impedance ofa homogeneous line; Fig; 2 shows ,the generalized network of this invention; 8 and 7 show two particular embodiments of the invention; Figs. 4, 5 and 6 show the simulation ofthe combined impedance of the network showngm F ig. 3 and a coil loaded line to the characteristie impedance of a homogeneous line for different values of K andCl, respectlvely; and Fi .6 shows the precision of simulation obtaina le with the network Fig. 7.

As shown in Fig. 1 the characteristicl impedance of such a line is simulated 1n a known manner by an olimic resistance having the value connectedseries with a wie.

condenser of the capacity When however the impedance of a coilV loaded line is to be simulated the problem becomes dlfiicult. vThe impedance of such a llne depends in a rather complicated manner upon the frequency and therefore requires ana-rrangement much more complicated for the simulation. An artificial line desi ed for this purpose has been indicated by S. Hoyt in the United States Patent No. 1,167 693. For many purposes, however, the necessity of being dependent upon the frequency is inconvenient. 1 The object of the invention hereinafter describedis to avoid this dependency by transforming the electric qualities of the loaded lines in such a manner that their impedance o becomes equal to that of a homogeneous aerial line, so that the simulation used .for

aerial lines may also be applied to loaded lines transformed according to the invention.

f The formula for the mid load characteris` tic impedance of a loaded 'line (see K. W. Wagner, Archiv fr Elektrotechnik, Band VIII, 1919, page 61 etc.) -is 2) w=\/R0 1LT. 1 W

iwCo 1 \/1 1Com (Ro lthat) In this formula RO=SR+R C0=8C, LO=SL+LB, where Rs and Ls denote the re- 75 sistance respectively the inductance of the coil and s the length of the-line between two coils. JThe influence of the capacity of the coillis so 'small that it may be neglected.

A mathematical simulation or close precision of the impedance is not necessary in practice. Divergences of 2% from the precise value are-allowable. VA simulation of greater precision would be of 'no avail, since in practice the real value differs about 2% from the theoretically calculated value of the characteristic impedance as a function of the frequency on account of structural inexactness in the construction of the lines and 90 the coils. These differences are sometimes positive and sometimes negative so that the formula for W (2) gives the mean value of theactual characteristic impedance.

Taking into consideration these relations the Equation 2 may. be brought into a form from which results the arrangement herein described. By a simple transformation and the substitution of the limiting frequency 11%; results of the Equation 2 (see K. W. Wagner above).

wo for 10 Lo Ro circ-.w

Ro 27Q;Lo 0.24 henry;

From these Values it results that in the dcnominator the term may be neglected as compared with the term up to near the limiting frequency. Then R02 of a2' Ro '4(1" 50)). c.;

Wz/A L., n.2 71002, l @i1-cav liar @iai For the terms of this equation the following values are obtained in employing the praclfray-10";

Above all the term R0:l 1Q-(2)3 may be neglected compared with the term 0 till near to the limiting frequency. Further the imaginary part amounts about to l/O of the real part; since with regard to the simulation the vector W is of particular importance, the influence of the imaginary part which is directed approximately at right angles to the vector is therefore very small and the correspondence of the two sides of the equation is not materially influenced, by

writing R0 R0 R01-JOC!) C0 w Cow 4 @cir a bei "Y1-ta?" tical values given above and for the frequencies w=7000 that is to say when the approximate formula G5 is ap lied.

With regard to this 1 L0 AIQW'ROIOL v o7,- ontl' 7 (A) i/l (a) )Vith the aid of the real relative values. the

radical may be dissolved as follows:

Leganes For long distance lines the impedance U1 is a given case, equal to the Vcharacteristic im 20 practically equal to the characteristic impedance. From the Equation 3 results 4) UF-tg, wherein I y C wo co wo From the Equations 3 and 4 it results that the impedance of the coil loaded line varies in a pedance. Further, by the present invention, the conditions are indicated according to Which such an arrangement is to be dimensioned for a given line.

According to Fig. 2 an auxiliary device is inserted before the impedance U1. G1 and G2 are impedances composed of condensers and inductances provisionally arranged in any desired manner. The values of these impedances may be written in the form Url and z'G2, WhereinG1 and G(a indicate real numerical values. The resistance at the ends of the net formed in this manner is U12'G1 f UFUHGI HG2 From the substitution of the expression (4) for U1 results n i'jti Glez c Glez The real constituent of the characteristic impedance of a homogeneous aerial line is independent of the frequency according to the Formula il. If this/shall also be true for U0, G1 in the Eqlpation (5) isto be chosen in such a manner t at l b '2L a (t) @t0-@Wea 'By this the Equation 5 is reduced to E -l-i b 2 a2. b 2 (ifea twee@ (t-GWT tibo-ei S a2 -I- iGz.

This value may be represented according to Flg. 1 by connecting in series an ohmic vrresistance and a capacity A simplel arrangement satisfying Within a practical suiciently large range the conditions 6 and Tis obtained for, instance by choosing for G1 (Fig. 2) a capacity K and for yG2" a parallel resonant circuit and an linduct- 1 L10 l G1- w, From this results for the Equation 6 This condition cannot be satisfied independently of the frequency in a mathematically precise manner. However from the use of approximated formulze results a satisfying mean correspondence of the two sides of the Equation 9 for K=O.32 CD. This shows also that the usc ofthe Equation 9 in first approximation is allowable, as for K=0.32 C0 the number neglected herein compared to l has for the important frequencies only a Value in the range of 3 10's.

For showing this correspondence, in Fig. 1, the calculated quotient of the two sides of the Equation 8 for K: 0.3 C., and K=0-325 C0 are represented as a function between the relation of frequencies The value 1 of the quo- If in this equation is substituted for L and Bite s lncwl-"w' This equation requires that Further the equation 2 1 L1C1w2z wo can be approximately satisfied by Fig. 5 shows the quotient of the two sides of the Equation 10 when the values found for tients corresponds to a Yprecise correspondence.

By the quotient is indicated according to its importance the degree of correspondence between the real portion of the changed impedance of the li ne and the constant ohmic resistance a: .qv/gi of the simulation. From K: (0.3 to 0.33) C.,

In exactly the same manner the values L Cl and L are obtained from the Equation 7. After substituting for G1, G2, a, Z) and c the expressions indicated hereabove in the Equa tion 7 it follows sa Www-0f 4m Fig. 3. Then the Equation 7 requires In' developing this equation members of the third power may still be taken into consideration and the values 0.854 C1 Llwo, are obtained.

Fig. 6 shows the precision obtainable in this way.

What I claim is:

l. A network for combining with a long 0.146 LILUOZ I equal within the range of transmitted frequencies to t-he characteristic impedance of a homogeneous line, said network comprising a capacity of value, K, of the order of 0.3 to 0.325 C0 in shunt to said line, an inductance of Value RoVLoCo and a parallel resonant circuit, said inductance Vand said parallel resonant circuit being connected in series with eachother and with the line, L0, Co and R0 being the total values of inductance, capacity, and resistance, respectively, per loading section of said line.

2. A network for combining with a long distance periodically loaded line to give to said combination an impedance substantially equal within the range of transmitted frequencies to the characteristic impedance of a homogeneous line, said network comprising a capacit of value, K, of the order of 0.3 to 0.325 o in shunt to said line, an inductance of value R01/Loco, 8

a parallel resonant circuit comprising an inductance of value, L1, equal to` KL0 200 and a capacity of Value, C1, equal to O -S Llwoz 7 and a second parallel resonant circuit comprising an inductance of value L1 and a capacity of value Llwoz,

In testimony whereof I allix my signature.

KARL KPFMLLER. 

